Question

Use the following scenario and data for all questions During lunch time, customers arrive at a postal office at a rate of per hour. The interarrival time of the arrival process can be approximated with an exponential distribution. Customers can be served by the postal office at a rate of per hour. The service time for the customers can also be approximated with an exponential distribution. For each of the following questions, show your work and use the right notation. Determine the utilization factor.

A) rho =4/5
B) rho =5/4
C) rho =2/3
D) rho=45-36=9
E) None of the above.
Determine the probability that the system is idle, i.e., no customer is waiting or being served.
A) rho_0= 4/5
B) rho_0= 5/4
C) rho_0=1/5
D) rho_0= 1/9
E) None of the above
Determine the probability that exactly one customer is in the system, i.e., no customer is waiting but one is served.
A) rho_1=1/9
B) rho_1=2/5
C) rho_1=1/5
D) rho_1=4/25
E) None of the above
Determine the probability that exactly one customer is waiting
A) p_2=2/81
B) p_2=16/125
C) p_2=4/125
D) p_2=4/25
E) None of the above
Determine the expected number of customers in the system including the one being served and the ones waiting in the queue
A) L=4
B) L=16/5
C) L=12/5
D) L=18/5
E) None of the above
Determine the expected length of the queue, i.e., the number of customer waiting in the queue.
A) L_q=4
B) L_q=16/5
C) L_q=12/5
D) L_q=18/5
E) None of the above

Answer 1

Check the explanation

Step-by-step explanation:

The assumptions in single-server queue theory include: -

1. Unlimited calling population may enter the queue
2. Arrivals occur randomly and are not dependent but average number of arrival does not change.
3. Single waiting line and arriving customers are patient customers who can wait in the queue before they can be served regardless of the length of the line.
4. Arrivals are serviced on a first come first served basis
5. Service time of one customer may vary from that of another customer.

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